I have asked this before, but I had no idea how to use Totient, now I do here is the questions:
How many positive integers $< 2013$ cannot be divided by $2, 3, 5$ ??
An advice given was find $\phi(2010)$
I got that:
$2010 = 2 \cdot 3 \cdot 5 \cdot 67$
But then $\phi(2010)$ would give the positive integers $< 2010$ that do not divide $2, 3, 5, 67$ the $67$ is the problem.
How can I use Totient to eliminate number that dont be divided by $67$ but can be by $2, 3, 5$ ?
No need to use $\phi$, simply apply inclusion/exclusion principle:
$2012-\lfloor\frac{2012}{2}\rfloor-\lfloor\frac{2012}{3}\rfloor-\lfloor\frac{2012}{5}\rfloor+\lfloor\frac{2012}{2\times3}\rfloor+\lfloor\frac{2012}{2\times5}\rfloor+\lfloor\frac{2012}{3\times5}\rfloor-\lfloor\frac{2012}{2\times3\times5}\rfloor$